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单词 SeparablyAlgebraicallyClosedField
释义

separably algebraically closed field


A field K is called separably algebraically closed if every separable element of the algebraic closureMathworldPlanetmath of K belongs to K.
In the case when K has characteristicPlanetmathPlanetmath 0, it is separably algebraically closed if and only if it is algebraically closed.
If K has positive characteristic p, K is separably algebraically closed if and only if its algebraic closure is a purely inseparable extension of K.

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更新时间:2025/5/4 8:48:48